Predicting how pollinator behavior causes reproductive isolation

Abstract Pollinator behavior is an important contributor to plants speciation, yet how variation in pollinator behavior causes variation in reproductive isolation (RI) is largely uncharacterized. Here I present a model that predicts how two aspects of pollinator behavior, constancy and preference, contribute to a barrier to reproduction in plants. This model is motivated by two observations: most co‐occurring plants vary in frequency over space and time, and most plants have multiple pollinators that differ in behavior. Thus, my goal was to understand how relative frequencies of plants and pollinators in a community influence ethological RI between co‐occurring plants. I find that RI for a focal plant generally increases with increasing relative plant frequency, but the shape of this relationship is highly dependent on the strength of pollinator behavior (constancy and preference). Additionally, when multiple pollinators express different behavior, I find that pollinators with stronger preference disproportionately influence RI. But, I show that RI caused by constancy is the average RI predicted from constancy of each pollinator weighted by pollinator frequency. I apply this model to examples of pollinator‐mediated RI in Phlox and in Ipomopsis to predict the relationships between plant frequency and ethological RI in natural systems. This model provides new insights into how and why pollinator specialization causes RI, and how RI could change with changing biological communities.

are most fruitful if the pollinator moves pollen between conspecific plants.
Speciation involves the evolution of reproductive isolating barriers between diverging lineages. Although there are many components to reproductive isolation (RI) in plants, pollinator behavior can be one of the strongest and most important (reviewed in Baack et al., 2015;Lowry et al., 2008). In many systems, pollinator behavior, as measured in the field, is strongly implicated in the process of plant speciation (e.g., Hopkins & Rausher, 2012;Kay & Schemske, 2003;Klahre et al., 2011;Ramsey et al., 2003;Schmid et al., 2016). Yet, there is still doubt as to the effectiveness of pollinator behavior in inhibiting reproduction and effectively driving speciation (Chittka et al., 1999;Waser, 1998). How can pollinators cause RI when most plants are generalists appealing to a variety of pollinators, and most pollinators are generalists visiting a variety of plants (Jordano, 1987;Ollerton, 2016;Robertson, 1928;Waser et al., 1996)? In order to better address this question, we need a framework for evaluating how quantifiable properties of pollinator behavior can contribute to RI in plants across complex communities.
Although pollinator-mediated RI between plants can result through both mechanical and behavioral mechanisms (Kay & Sargent, 2009), I focus here on two aspects of pollinator behaviorpreference and constancy-that can influence the amount of heterospecific pollen deposition and thus act as a barrier to reproduction.
Pollinator preference is the tendency of a pollinator to visit one species or variety of plant more than is expected based on that plant's relative frequency in a population. Preference can be expressed in response to an assortment of traits, such as color, size, shape, and smell, which often act as signals for a reward such as nectar (Schiestl & Johnson, 2013). Preference can cause RI, because in a community with two plant species, a pollinator that strongly prefers one species will transfer pollen between species of plants less than a pollinator that visits both species equally (e.g., Fulton & Hodges., 1999;Hoballah et al., 2007;Martin et al., 2008).
Pollinator constancy is the tendency of pollinators to move between the same species or variety of plant more than between different plants given what is expected based on the proportion of each plant visited (Waser, 1986). Constancy describes the order of visits to plants rather than the number of visits to each type of plant. High constancy can cause RI when pollen is transferred between conspecific individuals more than between heterospecific individuals.
Both constancy and preference are frequently measured in the context of plant speciation and both behaviors have been shown to cause strong RI (Campbell et al., 1997;Fulton & Hodges., 1999;Hopkins & Rausher, 2012;Kay & Sargent, 2009;Kephart & Theiss, 2004;Marques et al., 2007;Schemske & Bradshaw, 1999;Schmid et al., 2016). Most of these studies characterize patterns of pollinator behavior in a small number of locations, with controlled arrays of plants. Although this work strongly supports the important role of pollinators in plant RI, it is not currently possible to infer the strength of RI in natural populations that vary in the relative frequency of plant types and pollinator types. Furthermore, the relative importance of constancy and preference to plant RI has been debated in the literature (Kay & Sargent, 2009;Waser, 1998) but a direct comparison of their respective contributions has not previously been possible.
Co-occurring plant species vary extensively in relative frequency over space and time. Intuitively, the amount of pollinator movement between species is correlated with the relative frequency of plant species. If a population is predominately made up of one species, even with a pollinator moving randomly between plants, there will be fewer opportunities for transfer of pollen from the rare species to the common species than between the common species. But, we lack an understanding of how aspects of pollinator behavior, such as constancy and preference, affect RI across plant frequencies, especially given what is expected by random movement patterns.
Most of the flowering plants are visited by multiple pollinators (Robertson, 1928;Waser et al., 1996)

| One pollinator model
For a given pollinator i, the proportion of visits to a focal plant species ( i ) can be described as a function of pollinator preference ( i ) for the plant and the relative frequency of the focal plant (f).
Equation (1) is modified from a foraging preference function used by MacNair (1996, 1997). Here, preference varies from −1 (never visits focal plant) to 1 (only visits focal plant) with ρ = 0 indicating no preference such that the proportion of visits is equal to the frequency of the focal plant. This modification makes preference on the same scale as constancy. Preference for a given plant type is always relative to at least one other plant type in the community. This preference function can be adapted to include frequency dependent variation in preference (see Appendix B). Equation (2) is modified from the constancy formula presented in Gegear and Thomson (2004). I have modified this equation to calculate constancy to just a focal species instead of total constancy in a community including both species. Constancy varies between RI is defined as the reduction in heterospecific gene flow caused by a particular trait. I am interested in the reduction of heterospecific pollen movement caused by behavior (preference and constancy) and thus need to also calculate the expected heterospecific movement with no constancy and preference given plant frequency. In equation (3), if i and i are zero, then H i = (1 − f). To be consistent with standard measures of RI, as justified by Sobel and Chen, I define RI to vary from −1 (disassortative mating) to 1 (complete assortative mating) (Sobel & Chen, 2014). Thus, RI caused by pollinator i preference and constancy can be defined as: where (1 − f) represents the expected heterospecific movement for a given plant frequency with no pollinator preference and constancy.
Expanded, this simplifies to the following equation for RI: Using equation (4b), I determine how ethological RI varies across a focal plant's relative frequencies for no, strong, and weak pollinator preference and constancy. It is worth noting that based on this equation, preference and constancy will have equivalent effects on ethological RI. where H T is the total proportion of heterospecific pollinator visits By expanding H Tot , the total ethological RI can be predicted from pollinator behavior (preference and constancy), plant relative frequency, and the proportion of visits by pollinator 1 across the plant community. Expansion of Equation (7)

| Model applications
I apply this model to empirical datasets of pollinator behavior. Details of how to identify and calculate the necessary parameters from field observations are described in Appendix C.

| Pollinator preference and constancy for Phlox
Flower color divergence in P. drummondii is due to reinforcement (Hopkins & Rausher, 2012). A change in flower color, from lightblue to dark-red, evolved in sympatric populations in response to selection to increases RI between Phlox drummondii and P. cuspidata (Hopkins & Rausher, 2012 (1) and (2)

| Two pollinators' preferences for Ipomopsis
Ipomopsis aggregata and Ipomopsis tenuituba is a classically studied species pair for which pollinator behavior is known to play an important role in RI (Aldridge & Campbell, 2007;Grant & Grant, 1965).
These two species differ in several floral traits that influence pollinator preference such that hummingbirds prefer I. aggregata and hawkmoths prefer I. tenuituba (Aldridge & Campbell, 2007;Campbell, 2004). Based on the pollinator observation data reported in Table 1 of Aldridge and Campbell (2007), I calculate pollinator preference and constancy for each species at two natural locations of the Ipomopsis species and use equation (7) to estimate RI across plant relative frequencies and across proportion of pollinator visits.

| One pollinator model
In general, the strength of ethological RI increases with the strength of pollinator preference favoring a focal species (Figure 1).
With no preference, the proportion of heterospecific pollinator movements (H) is proportional to the relative frequency of focal plant and RI is zero (Figure 1a,d). When a pollinator has preference for the focal species, H is a decreasing concave function of relative plant frequency and RI is an increasing concave function of relative plant frequency, with the steepness of both curves determined by the strength of preference. When preference is strong ( = 0.8) and the focal plant is rare, small changes in plant frequency can result in large increases in RI. When preference is weak ( = 0.4), RI increases less with an equivalent change in plant relative frequency. Intuitively, this means that when a pollinator strongly favors a particular focal species it will continue to visit and transition between individuals of that focal species even as the plant becomes rare. When a pollinator has preference against the focal species, H is a decreasing convex function of relative As is evident in equation (4b), variation in constancy effects ethological RI in the same way as preference (Figure 1b,e). With positive constancy, RI increases with plant frequency, and with negative constancy RI decreases with frequency ( Figure 1e). Because of the equivalency of these two behaviors toward RI, a pollinator with strong preference and weak constancy causes the same proportion of heterospecific matings and RI as a pollinator with strong constancy and weak preference (Figure 1c,f). RI when one of its pollinators has no constancy than when a pollinator has negative constancy (black solid line is above the black dashed line, Figure 3c).

| Two pollinators' preferences for Ipomopsis
In a second example, I evaluate how H and RI between Ipomopsis taxa is predicted to vary across plant frequency given the polli-    The nonadditive contributions of two pollinators to RI reveals a mechanism for how pollinator specialization is favored. It has long been assumed, and observed, that if two closely related plant species attract different pollinators that express opposing preferences, then this specialization will result in RI between the plants (Fenster et al., 2004;Kay & Sargent, 2009). The advantage of pollinator specialization has been an emergent property in other theoretical models describing plant-pollinator communities (Sargent & Otto, 2006 (Keller et al., 2021;Ma et al., 2019

| Model applications
The results from my model provide  Figure 4b). This model can also make predictions about how hybridization will increase or decrease as climate change shifts plant and pollinator ranges, phenology, and population sizes (Memmott et al., 2007). For example, if a particular pollinator is predicted to decrease in abundance, RI for a plant preferred by that pollinator might actually be fairly stable until the pollinator is nearly extinct (as in Figure 1a). dependent preference (e.g., Cresswell & Galen, 1991;Gigord et al., 2001;Smithson & MacNair, 1996;Smithson & MacNair, 1997) and, as seen in Appendix A, this changes the shape of the RI function across populations. In other systems pollinators may vary their behavior depending on the behavior and frequency of other pollinators in the community (e.g., Brosi & Briggs, 2013;Fontaine et al., 2008;Inouye, 1978 Campbell et al., 2002) and in some systems this assumption is clearly violated (Ashman et al., 2004;Burd, 1994;Larson & Barrett, 2000). Extending the model to incorporate such scenarios is an important future direction and could easily be done by modifying equation (6). Depending on the specifics of a system of interest, an efficiency term that modifies either the proportion of visits to any plant in the community or the proportion of pollinator visits made to a focal plant could be added to the basic model presented here.
Previous theoretical research has considered aspects of plantpollinator community context to understand pollinator specialization, pollinator network structure (Bascompte et al., 2006), and how perturbations disrupt pollination (Kaiser-Bunbury et al., 2010;Memmott et al., 2004;Ramos-Jiliberto et al., 2012). Models such as these provide important insights into how and why plant-pollinator communities might be structured as they are and how their current structure can maintain biodiversity and community stability. Some of these models have even incorporated explicit aspects of pollinator behavior, such as adaptive foraging (Valdovinos et al., 2013(Valdovinos et al., , 2016. My model adds to this literature by specifically describing the implications of perturbations to pollination networks for speciation and potential hybridization.

| CON CLUS IONS
The goal of my model was to deconstruct the quantifiable aspects of pollinator behavior to understand how variation in behavior con-

O PE N R E S E A RCH BA D G E S
This article has earned an Open Data Badge for making publicly available the digitally-shareable data necessary to reproduce the reported results. The data is available at https://github.com/Phlox Hopki ns/Polli nator_RI_model.

DATA AVA I L A B I L I T Y S TAT E M E N T
All code for generating the model, running the model, and making the figures is available at https://github.com/Phlox Hopki ns/Polli nator_RI_model.